Kerodon

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Notation 4.3.3.9. Let $\operatorname{Fun}_{\ast }( \operatorname{Lin}^{\operatorname{op}}, \operatorname{Set})$ denote the full subcategory of $\operatorname{Fun}( \operatorname{Lin}^{\operatorname{op}}, \operatorname{Set})$ spanned by those functors $X: \operatorname{Lin}^{\operatorname{op}} \rightarrow \operatorname{Set}$ for which the set $X(\emptyset )$ is a singleton (that is, the full subcategory spanned by those functors which preserve final objects).